Chirality-selective transparency induced by lattice resonance in bilayer metasurfaces

Shuxia Zhao; Lei Shao; Jianfang Wang; Hai-Qing Lin; Wei Zhang

doi:10.1364/PRJ.416015

Abstract

Chiral optical responses of bilayer metasurfaces made of twisted metallic nanorods are investigated in detail with focus on the collective effect due to lattice resonance (LR). Using an analytical approach based on the coupled dipole method (supported by full wave simulation), we find optical chirality is dramatically increased by the coupling between localized surface plasmon resonances and LR. The collective effect results in significant chiral signal even for metasurfaces made of achiral unit cells. The interlayer coupling generally destroys the Wood’s anomaly and the associated transparency. While making use of Pancharatnam–Berry (PB) phase and propagation phase, one can modulate the optical activity effectively and achieve chirality-selective transparency induced by LR in a designed structure with a g-factor of absorption as high as 1.99 (close to the upper limit of 2). Our studies not only reveal a new mechanism of modulating chiral optical response by combination effects from PB phase, propagation phase, and LR, but also give a quantitative relationship between the geometry configuration and chiral optical properties, thus providing helpful guidance for device design.

1. INTRODUCTION

Chirality is of great importance in fundamental science, material design, biomedicine, and so on. Chiral optics associated with natural chiral molecules is limited by the fixed geometrical structure and weak optical signal mainly in the ultraviolet (UV) range. Plasmonic clusters supporting localized surface plasmon resonances (LSPRs) interact with visible light strongly, which can be controlled by the shape, size, position, and permittivity of the objects [1]. Plasmonic nanostructures can be precisely designed with complex geometric patterns and thus provide many opportunities for exploring light-matter/structure interaction, in particular the chiral nature of photonics. In the past decade, many types of chiral clusters have been explored to study circular dichroism (CD), such as helical particles [2, 3], tetramers [4], hybrid L-shaped resonators [5], U-shaped antennas [6, 7], hybrid rod-sphere structures [8], various dimers [9 - 14], and others [15, 16]. Using intrinsic chiral clusters as building blocks, chiral metamaterials/metasurfaces [17 - 23] can discriminate right- and left-circularly polarized (RCP and LCP) light, and they can even realize selective transmission of different circularly polarized light [24 - 26]. Furthermore, 2D planar metasurfaces with extrinsic chirality can realize asymmetric transmission/reflection [27 - 30] as well as modulation of light’s wavefront, direction, and polarization [31 - 34], which is promising in developing metalenses. The responses of metasurfaces of stacked layers are discussed in the view of photonic systems [19, 20, 35, 36]. Besides designing nanostructures, a structured light field (superchiral light) [37, 38] is proposed to increase light-material interaction, which is promising in amplification of chiral molecules’ CD signal [39].

Collective effects {such as lattice resonance (LR) [40 - 44]} and interference effects (such as Fano resonance [45] and electromagnetic induced transparency) modulated by electromagnetic (EM) field phase play important roles in controlling the optical properties. However, the study of the combination of those effects in the chiral metasurface area is in the preliminary stage [22, 46 - 51]. Many important issues need systematic studies. For example, it is known that the geometric configuration, such as the relative orientation/position of the substructure, affects the collective resonance [43, 50, 52], phases of the EM field {Pancharatnam-Berry (PB) [31, 53, 54] and propagation phase}, and mirror symmetry breaking (related to chiral response) [4, 14, 52]. Much effort is needed to investigate the physical consequence of the interplay of these effects, the resulting (chiral) optical properties, the applications in optics modulation, and device design.

Here we take an archetypical chiroptical nanorod dimer [9, 55] as the building block of the metasurfaces to explore the combination effects of collective resonance and interference on the chiral optics. Using an analytical approach based on a coupled dipole model (CDM) and finite-difference time-domain (FDTD) simulation, we find that the optical chirality of the metasurface is dramatically increased by the coupling between LSPRs and LR. The collective effect results in significant chiral signal, even for metasurfaces made of achiral unit cell-orthogonal nanorod dimers. By using phase (PB phase and propagation phase) modulated LR, different chiral responses can be obtained; in particular, chirality-selective transparency [100% transmission and a g -factor of absorption up to 1.99 (close to the upper limit of 2)] associated with Wood’s anomaly is realized in a specially designed structure, though in general the interlayer coupling destroys the Wood’s anomaly. Our studies reveal a new mechanism of tuning the chiral optical properties based on collective effect assisted by phase modulation (PB phase and propagation phase), and the analytical results (verified by numerical simulation) clearly reveal the quantitative relationship between the geometry configuration and chiral optical responses, providing modern photonic applications such as circular polarizers, optical communication, and quantum information processing.

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The paper is organized as follows. First we introduce the analytical formula to calculate the transmittance of metasurfaces. Second, we discuss the chirality of twisted nanorods and LR in monolayer metasurfaces. Third, bilayer metasurfaces’ extraordinary chiral transmission induced by LR is discussed and the general relationship between geometry and chiral optical response is given. Finally, we discuss the extraordinary chiral transmission of cases with higher-order resonance, square lattices, and the optical activity beyond the coupled dipole limit.

2. THEORETICAL FORMULA

A. Coupled Dipole Model

Scheme of the metasurface made of arrays of twisted nanorod dimers.

Figure 1.Scheme of the metasurface made of arrays of twisted nanorod dimers.

\frac{1}{α} P_{n}^{A} = {\hat{F}}_{A} \cdot (E_{n}^{A} + \sum_{m \neq n} {\hat{G}}_{n m}^{A A} P_{m}^{A} + \sum_{m} {\hat{G}}_{n m}^{A B} P_{m}^{B}), \frac{1}{α} P_{n}^{B} = {\hat{F}}_{B} \cdot (E_{n}^{B} + \sum_{m \neq n} {\hat{G}}_{n m}^{B B} P_{m}^{B} + \sum_{m} {\hat{G}}_{n m}^{B A} P_{m}^{A}),

D / E

x – y

k < \min {L_{x}, L_{y}}

T_{(0,0)} = \frac{P_{(0,0)}}{P_{inc}} = \frac{{| E_{0} e^{i k z} + E_{(0,0)}^{A} + E_{(0,0)}^{B} |}^{2}}{{| E_{0} e^{i k z} |}^{2}} = 1 - \frac{σ}{A} + \frac{k^{2}}{4 A^{2} {| E_{0} |}^{2}} {| P^{A} + e^{- i k z_{0}} P^{B} |}^{2} .

σ

R_{(0,0)} = \frac{P_{(0,0)}^{(R)}}{P_{inc}} = \frac{{| E_{(0,0)}^{A} + E_{(0,0)}^{B} |}^{2}}{{| E_{0} e^{i k z} |}^{2}} = \frac{k^{2}}{4 A^{2} {| E_{0} |}^{2}} {| P^{A} + e^{i k z_{0}} P^{B} |}^{2} .

A b = 1 - T - R

B. FDTD Simulation

x

α

3. RESULTS AND DISCUSSIONS

A. Optical Responses of a Single Nanorod Dimer and a Monolayer Metasurface: Localized Surface Plasmon Resonance and Lattice Resonance

Figure 2.Extinction cross sections of a dimer with twist angle $π / 4$ and separation $z_{0} = 200 nm$ for LCP and RCP light. Solid/dashed lines are the results calculated by CDM/FDTD.

θ

P_{L / R} = \frac{\sqrt{2} e^{\pm i θ}}{2 H (θ)} E_{0} (\cos θ {\hat{e}}_{x} + \sin θ {\hat{e}}_{y}) .

Figure 3.Transmittances of monolayer metasurfaces with $θ = 0, π / 6, π / 3, π / 2$ for LCP and RCP light.

B. Chiral Optical Response of Bilayer Metasurface: The Combination Effects from Lattice Resonance, PB Phase, and Propagation Phase

1. Chirality-Selective Transparency

θ

H (θ) = H (ϕ)

Figure 4.Transmittance of a bilayer metasurface with parameters $z_{0} = 200 nm$ , $Λ_{x} = 600 nm$ , $Λ_{y} = 300 nm$ . (a), (c) $θ = π / 3$ and $ϕ = π / 2$ ; (b), (d) $θ = π / 6$ and $ϕ = 5 π / 6$ . (a), (b) Results based on FDTD simulation; (c), (d) those based on the CDM.

{\hat{G}}_{x x}^{A A}

θ = π - ϕ = (π \pm k z_{0}) / 2

ϕ - θ = π / 2

Figure 5.(a), (b) Transmittance of a metasurface with achiral building blocks [i.e., unit cell with nanorod dimer of twist angle $π / 2$ ( $θ = π / 4$ and $ϕ = 3 π / 4$ )] based on FDTD simulation. (a) $Λ_{x} = 600 nm, Λ_{y} = 350 nm, z_{0} = 150 nm$ (the condition of chirality-selective transparency is satisfied); (b) $Λ_{x} = 400 nm, Λ_{y} = 350 nm, z_{0} = 150 nm$ (the condition of chirality-selective transparency is violated). (c)–(f) The electric field distribution ( $| E |$ ) for nanorods $A$ and $B$ at wavelength of 600 nm. (c), (d) The distribution at the $x – y$ cross-section plane with $z = 0$ (rod $A$ )/150 nm (rod $B$ ) for LCP light; (e), (f) the distribution at the $x – y$ cross-section plane with $z = 0 / 150 nm$ for RCP light. The other parameters are the same as those in (a). (g) The g-factor corresponding to (a). (h) The transmittance versus the long-axis radius of the nanorods at a wavelength of 600 nm.

λ = 600 nm

2. Higher-Order Lattice Resonance

Figure 6.Transmittance of LCP/RCP light associated with higher-order resonance based on FDTD simulation. (a) $θ = π / 4$ , $ϕ = 3 π / 4$ , $Λ_{x} = 1200 nm$ and $Λ_{y} = 300 nm$ , $z_{0} = 150 nm$ . $k = | L_{(\pm 2,0)} |$ . (b) $θ = π / 4$ , $ϕ = 3 π / 4$ , $Λ_{x} = 931 nm$ and $Λ_{y} = 781 nm$ , $z_{0} = 150 nm$ . $k = | L_{(\pm 1, \pm 1)} |$ .

k = | L_{(0, \pm n)} |

k = | L_{(\pm n, \pm m)} |

3. Bilayer Metasurface with Square Lattice

Λ_{x} = Λ_{y}

θ = ϕ

ϕ - θ = π / 2

4. Beyond Coupled Dipole Approximation

Figure 7.Transmittance of LCP/RCP light with $Λ_{x} = 600 nm$ and $Λ_{y} = 350 nm$ calculated by the FDTD method. (a) $z_{0} = 90 nm$ , $θ = 7 π / 20$ , and $ϕ = 13 π / 20$ . (b) $z_{0} = 75 nm$ , $θ = 3 π / 8$ , and $ϕ = 5 π / 8$ .

4. CONCLUSION

θ = π - ϕ = \frac{π \pm k z_{0}}{2}

References

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